So you are looking for something like this?
That's possible with virtually any waveform generator that supports Pulse mode (N Cycle) or, though maybe not as accurately phase-wise, amplitude modulation with a square wave.
It's up to you to define "inexpensive" or "cheap"... The screenshot shown has been generated with a hacked Rigol DG811, which I'ld currently consider the best option from a value-for-money point of view, but any entry level AWG, be it Siglent or Rigol, will do. I'm not familiar with the UNI-T and the Feeltech or similar "Tinkerer's Delight" boxes, but it's well possible that they will suit your needs at two-digit price tags as well. So I recommend to search the forum for the related threads and get yourself an opinion of the available models.